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Lecture 12 Content

Stereoscopic parallax

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Nadir and Isocenter on a photo– Nadir: point vertically beneath the camera lens at the time

of exposure (where a plumb line extended from the camera lens to the ground intersects the photo image)

– Isocenter: point on the photo that falls on a line approximately halfway between the principal point and nadir

Nadir Isocenter

Principal Point

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K-Factor– The ratio of the air base length to the

altitude at which a pair of aerial photographs were taken (i.e. B:H)

B

O1 O2

Terrain

H

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Stereoscopic parallax– Parallax is the distance between images of

the same object on the two photographs forming a stereopair

x

z

y

A1 A2

A1

A2

py

px

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– Stereoscopy refers to the ability to perceive the object space in three dimension using your two eyes

– Using one eye, a person’s perception of depth is hampered

– Using one eye monocular viewing– Using two eyes binocular viewing– Binocular viewing allows the viewing from

two different locations due to the separation between the eyes (eye base)

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Convergence angle

– Because angle Φ1 is larger than Φ2 the observer will perceive point P1 as closer than point P2

– difference in distance from observer, (H2-H1=h) is a function of the difference in convergence angle, Φ1- Φ2

Φ1

Φ2

bL R

P2

P1

H1

H2

h

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Comparing binocular and stereoscopic viewing

Φ1

Φ2

bL R

P1

H1

H2

h

b

Φ1

Φ2

L R

h

Convergence Angle Stereoscopic Viewing

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– Angle Φ is called the parallactic angle and its linear equivalent is called parallax

– Assuming no tilts, both photos are taken at the same altitude, and any rotation of the camera from one photo is accommodated by replacing the fiducial system of axis by another, then the x parallax (or simply parallax) is defined by:

P =x-x´– Where x and x´ are the coordinates on the left and

right photographs

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– Stereoscopic parallax enables perception of height differences

– This is defined by the x-parallax– Y-parallax once removed, defines the

straight line between two consecutive photos

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Height difference using parallax

Datum

p a

xf f

x´

(H-h)

Air Base = B

c1 c2

E E´

Ah

a´

a´

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– Photos are H above the datum

– Point A is h above the same datum

– Coordinates x and x´ are defined by the location of a and a´ on image using the principal point on each photo as the origin

– That is C1a´ is equal to x´

– Parallax (p) is given by x - x´ and is the line segment a´a

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∆ aa´E and ∆ EE´A are similar:

p

fBHh

p

fBhH

p

B

f

hH

f

p

hH

B

To determine elevation of point A requires:Flying heightValue of air baseCamera focal length

Datum

p a

xf f

x´

(H-h)

Air Base = B

c1 c2

E E´

Ah

a´

a´

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Determining the ground coordinates of a point with respect to an arbitrary coordinate system whose origin is vertically below the left exposure station and with a positive X in the direction of flight

Datum

p a

xf f

x´

(H-h)

Air Base = B

c1 c2

E E´

Ah

a´

OXA

Flight direction

Ground Coordinates formulae:

a´

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– Triangles EOA & EC1a are similar

– Coordinate for A is (XA,YA) using the arbitrary coordinate system:

(x is the distance on the photo for point “a”)

f

hHxX

f

x

hH

X

A

A

)(

Substituting for h (derived before), we get:

p

ByY

and

p

BxX

A

A

Datum

p aa’

xf f

x´

(H-h)

Air Base = B

c1 c2

E E´

Ah

a´

O XA

Flight direction

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– Recall scale (S) at a point of elevation is given by:

)( hH

fS

– Substituting for h which is defined by the parallax height equation into the scale equation gives:

B

pS

p

fB

fS

p

fBHH

fS

This is the map scale defined as a function of the parallax and air base

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Parallax Measurement (Manual method)– Two photographs are fastened to a base aligned along the

flight line– The flight line is derived by locating the principal points of

the two photographs. Each photo with have two points (one for its principal point and the other principal point for the neighboring photo). Connecting these four points a straight line will be formed which is indicative of the flight line

– Parallax can then be measure from a single measurement using a parallax bar (Such a bar measures the linear distances at a very high accuracy)

– The distances measured are used in the equations derived previously

– Once the photographs are properly secured and is in line with the flight line, the distance between the two principal points between the two photographs is measured and noted

– Parallax is then measured off by selecting identifiable common points on the two photographs

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Positive ‘x’ distance from the principal point

Negative ‘x’ distance from the principal point

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… The End …